If \(\left[\begin{array}{ll}x-y & 0 \\ x+y & 1\end{array}\right]\) is an identity matrix and \(\left[\begin{array}{ll}x & y \\ x & x\end{array}\right]\) is a singular matrix then :

The relation R in R (set of real numbers) is defined by \(R=\left\{(a, b): a \leq b^3\right\}\), then \(R\) is

In a college, 30 % students fail in Physics, 25 % fail in Mathematics and 10 % fail in both. One student is chosen at random. The probability that she fails in Physics if she has failed in Mathematics is

The value of \(\left|\begin{array}{ll}\sqrt{3} / 2 & 1 / 2 \\ \sqrt{3} / 2 & 1 / 2\end{array}\right|\)

Consider the LPP, Max Z = x + y subject to the conditions
\(x+y \leq 3, \quad x-y \geq 1, \quad x \geq 0, y \geq 0\),
then which of the following is not the corner point of the feasible region of above LPP.

\(\sin ^{-1}\left(\cos \frac{3 \pi}{5}\right)\) equals

The equation of normal to the curve \(2 y+x^2=3\) at the point (1, 1) is:

Read the given paragraph and answer the question:
Humans have 23 pairs of chromosomes. 22 pairs are exactly same in both males and females; these are the autosomes. A pair of X-chromosome are present in the female, whereas the presence of an X and Y chromosome are determinant of the male characteristic.
A number of disorders in human beings have been found to be associated with the inheritance of changed or altered genes or chromosomes. Broadly, genetic disorder may be grouped into two categories-Mendelian disorders and Chromosomal disorders
A colour blind man marries a carrier woman. Choose the possible progeny outcome.

Match List - I with List - II.

List – I	List – II
(A) Ethanol and Diethyl ether	(I) Lucas reagent
(B) Methanol and Ethanol	(II) Sodium metal
(C) n-Butyl alcohol and tert. Butyl alcohol	(III) Iodoform test
(D) Phenol and Cyclohexanol	(IV) Ferric Chloride

Choose the correct answer from the options given below :

Match List - I with List - II.

LIST-I (Equation of curves)	LIST-II (Slope of tangent at \(x=2\))
(A) \(y=x^3-x\)	(I) 8
(B) \(y=(x-2)^2\)	(II) \(frac{2}{3}\)
(C) \(y=2 x^2+3\)	(III) \(11\)
(D) \(y=\sqrt{4 x+1}-7\)	(IV) \(0\)

Choose the correct answer from the options given below :

Observe the figures and answer the question.

Why is it that most zygotes divide only after certain amount of endosperm is formed?

The overhead horizontal power transmission line carries a current of 75 A from east to west direction. The magnetic field above it at a vertical distance of 1.2 m will be

Match List - I with List - II.

LIST I	LIST II
(A) Polyembryony	(I) Apple
(B) Parthenocarpy	(II) Female gametophyte
(C) False Fruit	(III) Orange
(D) Embryo Sac	(IV) Banana

Choose the correct answer from the options given below :